I have read multiple explanations of escape velocity, including that on Wikipedia, and I don't understand it.
If I launch a rocket from the surface of the Earth towards the sun with just enough force to overcome gravity, then the rocket will slowly move away from the Earth and we see this during conventional rocket launches.
Let's imagine I then use slightly excessive force until the rocket reaches 50 miles per hour and then I cut back thrust to just counterbalance the force of gravity. Then my rocket will continue moving at 50 mph toward the sun. I don't see any reason why I can't just continue running the rocket at the same velocity and keep pointing it towards the sun. The rocket will never orbit earth (by "orbit" I mean go around it). It will just go towards the sun at 50 mph until it eventually reaches the sun. There seems to be no need whatsoever to ever go escape velocity (25,000 mph).
Answer: just to clarify the answers from below and the other linked question... Escape velocity is not necessary to leave the earth, unless the object has no thrust or other means of propulsion. In other words, if you throw a baseball, it has to go escape velocity to leave the earth, but if you have a spaceship with engines, then you leave the earth at any speed you want as long as you have the fuel necessary.